SOLUTION: logx (2x + 5) = 2

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Question 194220: logx (2x + 5) = 2
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
logx (2x + 5) = 2
(2x + 5) = x^2
0 = x^2 - 2x - 5
.
Solving with the quadratic equation yields:
x = {3.449, -1.449}
We can toss out the negative solution leaving:
x = 3.449
.
Details of quadratic follows:
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-5=24.

Discriminant d=24 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+24+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+24+%29%29%2F2%5C1+=+3.44948974278318
x%5B2%5D+=+%28-%28-2%29-sqrt%28+24+%29%29%2F2%5C1+=+-1.44948974278318

Quadratic expression 1x%5E2%2B-2x%2B-5 can be factored:
1x%5E2%2B-2x%2B-5+=+1%28x-3.44948974278318%29%2A%28x--1.44948974278318%29
Again, the answer is: 3.44948974278318, -1.44948974278318. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-5+%29